Evaluate the integral as
[tex]\lim_{b\rightarrow \infty}\int_{a+1}^{b}\frac{1}{\frac{1}{a}-\frac{1}{x}}\ {dx}[/tex]
[tex]=\lim_{b\rightarrow \infty}\int_{a+1}^{b}a-\frac{a^2}{a-x}\ dx[/tex]
...
... you can do the intermediary steps here... you'll work out that you get something like the following:
[tex]\lim_{b\rightarrow \infty}ab-a^2\log{a-b}-a^2-a+\log{1}[/tex]

as you know, [itex]ab[/itex] goes to infinity as b goes to infinity. ln(a-b) also becomes undefined as you subtract infinity from any number, since log is only defined for positive numbers.